After Thelin condemned the actions of the fan in question as “unacceptable”, Aberdeen released a statement describing themselves as “dismayed and outraged”.
The club said they know “for sure” the seat thrown came from the part of the stand that their fans were housed in.
And they urged any supporters with information to contact the club and vowed to take “the strongest possible action available to us” if a culprit is identified.
The Aberdeen support at Tannadice was already restricted in number after objects were aimed at United manager Jim Goodwin – who was previously in charge at Pittodrie – in the last meeting at Tannadice.
United are yet to comment on the incident, but Goodwin – who was also targeted in a game last season – labelled the scenes “a disgrace”.
“I deliberately took myself off the pitch as quickly as I could because we’ve had previous with the Aberdeen supporters,” he said.
“I’m really disappointed to hear young Jack has been hit by an object thrown by his own supporters. He’s inside having stitches now, it’s an absolute disgrace.
“It’s probably taken something as serious as this to happen for the authorities to finally step in and do something about it to identify these idiots who let down a really good club.”